You saw this, right?

https://wiki.haskell.org/Nitpicks#Base-related_nitpicks

(Just in case, maybe it was you who included this topic.)

Alexey.

On Monday, September 7, 2015 at 4:08:54 PM UTC+2, DreamApart AtHaskells wrote:

The class Num defines the method functions like (+), (-), (*), negate, ...

But they are actually different concepts.

We often meet situations that we want an addition for some type, but

not a multiplication. For example:

    data Vec3 = Vec3 Float Float Float

The additive (and subtractive) operation is obvious, but not for a

multiplication.

  Note

    (*) :: a -> a -> a   -- not avaliable for a Vec3

    scale :: Float -> Vec3 -> Vec3

    dot :: Vec3 -> Vec3 -> Float

We cannot define a (+) alone for a type, so we got many different functions

from different libs, like mappend, mplus, plus, (<+>), (.+.), (+.), which all reads

"plus".

My opinion is that the methods of Num should be seperated into different type

classes, so we don't need to invent a new symbol for a new lib.

A feasible design is:

    import Prelude hiding ( Num (..), Monoid (..), sum )

    class SemiGroup a where

        (+)         :: a -> a -> a

    class SemiGroup a => Monoid a where

        zero        :: a

    

    class Monoid a => Group a where

        negate      :: a -> a

        (-)         :: a -> a -> a

        x - y    = x + negate y

        negate x = zero - x 

    class Group a => Ring a where   -- not sure about the name ...

        (*)         :: a -> a -> a

    

    class Ring a => Num a where

        abs         :: a -> a

        signum      :: a -> a

        fromInteger :: Integer -> a

    sum :: (Foldable t, Monoid a) => t a -> a

    sum = foldl' (+) zero

    -- for compatibility 

    mempty = zero

    mappend = (+)

    mconcat = sum